Tidal Love Numbers of Kerr Black Holes

TL;DR

This paper investigates the tidal deformability of Kerr black holes by computing their tidal Love numbers, revealing that nonaxisymmetric perturbations induce measurable multipole moments and linking these to tidal torquing effects.

Contribution

It provides the first explicit calculation of rotational black hole tidal Love numbers for nonaxisymmetric perturbations and introduces the concept of a tidal Love tensor.

Findings

Linear response vanishes for Schwarzschild black holes.

Nonaxisymmetric perturbations induce non-zero multipole moments.

Induced quadrupole moments relate to tidal torquing phenomena.

Abstract

The open question of whether a Kerr black hole can become tidally deformed or not has profound implications for fundamental physics and gravitational-wave astronomy. We consider a Kerr black hole embedded in a weak and slowly varying, but otherwise arbitrary, multipolar tidal environment. By solving the static Teukolsky equation for the gauge-invariant Weyl scalar $\psi_0$, and by reconstructing the corresponding metric perturbation in an ingoing radiation gauge, for a general harmonic index $\ell$, we compute the linear response of a Kerr black hole to the tidal field. This linear response vanishes identically for a Schwarzschild black hole and for an axisymmetric perturbation of a spinning black hole. For a nonaxisymmetric perturbation of a spinning black hole, however, the linear response does not vanish, and it contributes to the Geroch-Hansen multipole moments of the perturbed Kerr geometry. As an application, we compute explicitly the rotational black hole tidal Love numbers that couple the induced quadrupole moments to the quadrupolar tidal fields, to linear order in the black hole spin, and we introduce the corresponding notion of tidal Love tensor. Finally, we show that those induced quadrupole moments are closely related to the well-known physical phenomenon of tidal torquing of a spinning body interacting with a tidal gravitational environment.